Question

the sides of a triangle are shown. determine if the triangle is a right triangle. 20, 21, 29

Explanation:

Step1: Recall Pythagorean theorem

For a right - triangle with sides \(a\), \(b\), and hypotenuse \(c\), \(a^{2}+b^{2}=c^{2}\). Let \(a = 20\), \(b = 21\), and \(c = 29\).

Step2: Calculate \(a^{2}+b^{2}\)

\(a^{2}+b^{2}=20^{2}+21^{2}=400 + 441=841\).

Step3: Calculate \(c^{2}\)

\(c^{2}=29^{2}=841\).

Step4: Compare

Since \(a^{2}+b^{2}=c^{2}\) (i.e., \(841 = 841\)), the triangle is a right - triangle.

Answer:

Yes, the triangle is a right - triangle.